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Probabilistic Projections of HIV Prevalence Using Bayesian Melding

The Joint United Nations Programme on HIV/AIDS (UNAIDS) has developed the Estimation and Projection Package (EPP) for making national estimates and short term projections of HIV prevalence in countries with generalized epidemics. This combines a mechanistic epidemiological model with prevalence data from antenatal clinics and from household surveys.

Understanding uncertainty in its estimates and projections is important for policy, and UNAIDS now uses Bayesian melding as the basis for its probabilistic projections of HIV prevalence. Initially, the posterior distribution was approximated by sampling-importance-resampling, which is simple to implement, easy to interpret, transparent to users and gave acceptable results for most countries. For some countries, however, this is not computationally efficient because the posterior distribution tends to be concentrated around nonlinear ridges and can also be multimodal. We propose instead Incremental Mixture Importance Sampling (IMIS), which iteratively builds up a better importance sampling function. This retains the simplicity and transparency of sampling importance resampling, but is much more efficient computationally. It also leads to a simple estimator of the integrated likelihood that is the basis for Bayesian model comparison and model averaging. In simulation experiments and on real data it outperformed both sampling importance resampling and generic MCMC algorithms.

This is joint work with Leontine Alkema, Le Bao and Sam Clark.